International Journal of Mechanical and Materials Engineering (IJMME), Vol.x (xxxx), No. x,xxx

STEADY STATE ANALYSIS OF COOLANT TEMPERATURE DISTRIBUTION IN A

SPARK IGNITION ENGINE COOLING JACKET

M.A. Hazrat, H.H. Masjuki, M.A. Kalam, I.A. Badruddin, R. Ramli and S.C. Pang Centre for Energy Sciences, Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,

50603 Kuala Lumpur, Malaysia

Corresponding author’s E-mail: alihazrat20@yahoo.com

Received 09 January 2013, Accepted 12 January 2013

ABSTRACT

A full scale SI engine has been imported in to the CFD

tool to analyse the temperature distribution of coolant

throughout the cooling channels. The segregated

approach solver has been adopted to solve the energy

equations along with the RANS two layer turbulence

model to find out accordance with the available

theoretical and published results. The input values are

collected from complete vehicle test and from available

documents, too. The main objective of the analysis was

to observe the coolant temperature distribution inside the

cooling jacket when the engine is turned off. The steady

state simulation shows that though the average coolant

outlet temperature is found within the acceptable limit of

cooling system operation principle, there is a large

temperature gradient in fluid thermal boundary layers

within cross section and overall jacket path. The analysis

demands that there should be some special arrangement

of maintaining the fluid flow inside the cooling jacket

even after the engine is turned off to avoid further loss of

the engine body due to high temperature accumulation

inside the cooling jacket and fluid in it. The lump

capacity conduction equation for first sec shows that the

wall temperature obtained through the energy equation is

in accordance with it, too.

Keywords: SI engine heat transfer, Coolant temperature,

Steady state heat transfer, CFD, Segregated approach

NOMENCLATURE

Symbols

k Thermal conductivity (W/m.K)

C Specific heat capacity (J/kg.K)

Pr Prandtl number

q Heat flux (W/m2)

u Wall-cell velocity component parallel

to the wall (m/s)

T Temperature (K)

y Normal distance from the wall (m)

x Distance (m)

V Volume (m3)

S Source energy

lc Characteristic length

v Velocity vector

T Viscous stress tensor

H Total enthalpy (J/kg)

q Heat flux vector

E Total energy (W)

u+ Dimensionless velocity

t+

Dimensionless temperature

Greek symbols

μ Viscosity

ρ Density (kg/m3)

τ Shear stress (Pa)

Subscripts

c Coolant

e Effective

g Gravity (m/s2)

p Constant pressure

s Solid

t Turbulent

w Wall

ref Reference level

1. INTRODUCTION

Internal combustion engine heat transfer analysis thus

improving the removal of excess heat from the engine

thermal system and leading to the improvement of engine

thermal efficiency has been considered as one of the

scientific challenges for decades. Various types of engine

geometry and fuels, operation principle, high temperature

and high speed of both the crank shaft as well as the

pistons inside the cylinder, etc. are the challenging

factors Demuynck et al.(2009) in developing globally

acceptable model for engine heat transfer, i.e. effective

thermal management system. Characterizing the engine

as well as the vehicle thermal system management,

reduction of emissions and fuel demand per crank shaft

rotation and load governance, etc. are analyzed both in

experimentally and theoretically Torregrosa et al.(2008).

Theoretical analysis of heat transfer from combustion

chamber to the surrounding areas i.e. water jackets in

both the cylinder blocks and cylinder heads require

appropriate solution of continuity, momentum and

energy equations Borman and Nishiwaki(1987). Solution

of these equations is not easy to perform and therefore,

various computational codes have been developing to

perform such calculations. When the analytical results

are found in accordance with the available experimental

data the conceived numerical model is considered as a

benchmark to improve the real model through

computational analysis.

Liquid cooling system of an internal combustion engine

is sometimes dealt as the channel flow system and the

heat transfer coefficient for convective mechanism is

calculated through those equations (Çengel, 2002; Dittus

and Boelter,1930; Heywood, 1988; Ozisik,

1980;Rohsenow and Griffith, 1955; Sieder and Tate,

1936). Moreover, the experimental investigations are

performed through temperature measurement of the

coolant in the jackets inserting various thermocouples in

various points. In an actual sense, the heat transfer and

temperature distribution is varied in every point of the

cooling jacket. An extensive CFD model employing the

energy equations for both fluid and solid parts can help

providing with such results if proper boundary conditions

can be used. The industrial researches on automotive

cooling system development claims the CFD analysis as

one of the effective and faster approaches and it can

provide some key information which are not accessible

through the experimental works like special issues: warm

up, idling and key-off temperature conditions of the

coolant in cooling jacket (Fontanesi et al., 2010; Jasak et

al., 1999; Shibata et al., 2004).

2. PROBLEM STATEMENT

When an engine is keyed-off after a long time of full load

travel for a few minutes like in traffic or in parking, the

residual heat of the engine combustion chamber is

conducted to the stagnant hot coolant inside the coolant

jacket. Since modern internal combustion engines are

designed to run under precision cooling mechanisms,

coolant is already circulated through the jacket in higher

temperature near to boiling point based on the working

pressure. This excess heat can’t be carried out to the

radiator as the actuators are idle/ stopped as soon as the

engine is in idle condition, thus resulting sudden

temperature rise of the coolant and it leads to severe

coolant spill out, too due to the high pressure generated

from the produced vapours or boiling bubbles.

Piccione and Sergio (2010) have described this problem

stating that, as the engine is shut downand coolant flow

stops thus the engine is brought down in an idle

condition for 5sec to 80sec, the head metal may be

hotenough to vaporize a fraction of the coolant contained

inthe cylinder head passages, causing the pressure within

the coolingcircuit to rise above the threshold value of the

radiatorcap pressure valve and, consequently, an

important quantity of thecoolant to be expelled. A few

researchers (Chastain, 2006; Allen et al., 2004; Ap and

Tarquis, 2005; Chominsky and Dehart, 2010; Franchetta

et al., 2006; Piccione and Sergio., 2010; Bova et al.,

2004) have already noticed this phenomena and few

resolutions are proposed by them too. Here in this article,

an internal combustion engine model has been contrived

to investigate the temperature distribution of the coolant

inside the cooling jacket through CFD based steady state

analysis. The problem is considered as conjugate heat

transfer mechanism. Therefore, only a few input

boundary conditions required to use the energy equations

in computational codes. Steady state heat transfer and

temperature distributions may help providing the insight

of the coolant, coolant-solid interfaces and coolant side

walls in a point to point basis. The steady state CFD

simulation can guide the automotive design engineers as

well as the manufacturers to find out required resolution

to devise to resolve any harmful events due to heat

transfer from the combustion chamber walls to the

cooling jacket coolant after key-off.

3.MODELING THE PHYSICS

The researchers are generally inclined to avoid the

computational intricacies of employing energy equations

in modelling the heat transfer phenomenon of engines

due to data insufficiency (Nijeweme et al., 2001;

Nuutinen, 2008; Torregrosa et al., 2008); rather they

easily use either the experimental correlations or

empirical correlations obtained from dimensional

analysis while modelling internal combustion engine

cylinder heat transfer to the coolant. But here in this

analysis, the energy equation is employed to observe the

temperature distribution of the coolant in the water

jacket.

Following the assumptions of incompressible fluid and

simplified numerical modeling of actual Navier-Stokes

models, the “Realizable k-ε Two-Layer turbulence”

model by Shih et al.(1994) has been adopted for this

simulation.Wolfstein(1969) model has been utilized here

as “Two-Layer model formulation”. This model can

satisfactorily resolves the issues of normal stress

constraints with consistency on physics defined by

turbulent flows. The success of this equation over the

other standard k-ε models is that it can well analyse the

prediction of axisymmetric jet’s spreading rate as well as

planar jets; and it has wide spread validity on channel as

well as boundary layer flows with same ability on

separated flows, too. The realizable model computes the

thermal conductivity of the material by

,

with a constant turbulent Pr value of 0.85. The wall heat

flux is thus computed as,

(

)

( ) (1)

In a non-dimensional approach the wall laws are related

to,

(

)

(√

⁄ )

(2)

Here, y is the normal distance from the wall to wall cell-

centroid, u is the wall-cell velocity component parallel to

the wall, T is the fluid cell temperature near wall, Tw is

the wall-boundary temperature, q is the heat flux, is the

fluid reference average velocity, is the kinematic

viscosity, is the wall shear stress.

The wall function also provides the heat transfer

coefficient as follows:

( )

(

)

( )

( )

( )

⁄

⁄

( )

(3)

The turbulence model (RANS) is then mixed with the

energy equations, continuity equations and momentum

equations. The combined model is formulated and run in

a solver’s solutions process. Here, both the velocity and

the pressure components are analysed separately in the

segregated flow model solver CD-Adapco (2011),

Trottenberg et al.(2001). The methodology is also known

as uncoupled solution and the predictor-corrector

approach is employed to link the momentum as well as

the continuity equations to define the cases with

continuity equations. Generally, the segregated approach

is considered as co-located (where the pressure and

velocity are considered to be in the same location, it is

not staggered) but the Rhie-and-Chow (1983) type

pressure-velocity coupling combined with a SIMPLE-

type algorithm Patankar(1980) are employed for

advection velocities (where the cell-faces’ velocities are

utilized to compute the mass fluxes). This model is

appropriate for incompressible fluid flows (constant

density flows) and can compute the compressible fluids

with low Mach number (less than 0.3) and few natural

convection problems but this is not capable of capturing

shocks in the high Mach number compressible fluid

flows or high Raleigh-numbered fluid dynamic

applications. A second order upwind convection scheme

is used for the convective flux computation in the

governing equation for better convergence.

The governing equations for continuity and momentum

(in integral form) can be presented as follows

respectively;

∫

∮ ( ) ∫ [ ]

(4)

∫

∮ ( )( ) ∮

∮

∫ ( )

(5)

The transient as well as the convective flux terms are on

the left side of the equation (5); whereas, the gradients

due to pressure, viscous flux (due to viscous stress

tensor, T) and the body forces (f) due to gravity (g), user

defined (u) and other type of body forces like vorticity

confinement (ω) respectively are in the right side.

The “Total Energy Equation” for fluid flow can be

presented in integral form as follows:

∫

∮ [ ( ) ] ∮

∮

∫

∫ (6)

Here, E is the total energy, H is total enthalpy, q is the

heat flux vector, T is the viscous stress tensor, v is the

velocity vector, vg is the velocity vector for grids, f is

body force vector; Su is the energy source as user

defined.

It is to be noted that the total energy equation for the

solid model in the segregated solid energy model can be

expressed as follows:

∫

∮

∫

(7)

Here, is the solid density, is the solid’s specific

heat capacity, is the solid’s temperature, q is the heat

flux vector and S is the energy source as defined.

3.1 Boundary conditions

Mass flow inlet: 1.3 kg/s (i.e. 78 L/min),

Pump capacity: 80 L/min.

Coolant inlet temperature: 355 K (i.e. 82 0C)

Coolant: Water (water has higher specific heat capacity

than 50/50 EG-H2O)

Initial pressure: 1.2 bar (gauge) (i.e. boiling point is >401

K)

Temperature of the combustion chamber walls, the

cylinder head skirts and the exhaust manifolds: 600 K

(i.e. 327 0C)

Materials: Cylinder block (Fe) and Cylinder head (Al)

3.2 Assumptions

The CFD simulations were performed in steady state

conditions. The fluid was coolant (50/50 Ethylene

glycol-H20) and the simulations were performed

considering the wall surfaces as smooth for the coolant

flow. Several cases for combustion chamber wall

temperature were considered to check the fluid flow heat

transfer and temperature distribution. In all cases, it was

considered that the heat transfer from the cooling jacket

side walls to the flowing coolant is fully a forced

convective mechanism. Since there is an improvement of

BSFC (Brake Specific Fuel Consumption) due to

maintaining a higher temperature of combustion chamber

walls (about 4-6% improvement due to 80-100 OC more

than the usual consideration of wall temperature Rehman

et al.(2010), the wall temperatures are mainly considered

as of 573K, 600K and 773K (for high speed engines)

ranges for the combustion side hot walls (Rakopoulos et

al., 2008; Idroas et al., 2011).

The fluid (coolant: H2O - Ethylene glycol) properties

were considered to be as the incompressible fluid

properties (i.e. constant properties). The corresponding

boundary conditions are presented in the following

sections of analysis.

4. RESULT AND ANALYSIS

Figure 1 Cross sectional view of engine cooling jacket.

A schematic of the cooling jacket geometry is shown for

internal combustion engine (Figure 1). The steady state

simulation is performed with the value of the order 10-7

for theresidual terms when it is stabilize by solving the

required energy equations in the segregated approach.

There were about 25 million volume cells in the solid

parts and 4.6 million volume cells in the liquid continua

of the engine’s physical model. The result of coolant

temperature distribution is presented here to observe their

effect in those regions.

4.1 Temperature distribution

The flowing water carries the heat from the walls while

flowing through the cooling jackets. The corresponding

wall temperature and coolant temperature are shown in

the “Figure 2” and “Figure 5”.

Figure 2 Temperature distribution of 1.3 kg/s coolant flow heat transfer.

Figure 3 Velocity distribution of water (1.3 kg/s) in the cooling jacket.

From the analysis of fluid flow and heat transfer in an

internal combustion engine where the water is used as a

coolant shows a good temperature distribution; though

high temperature boundary layers are found showing the

boiling action (since the temperature is beyond boiling

point of coolant used) in the thin layers of the fluid in

contact with the hot side walls. Because of the simplified

flow in the block jacket the heat transfer coefficient is

showing almost a constant value in this section “Figure

4”. But the value found is a surface average quantity. In

actual cases, the fluid near to the hot walls shows higher

heat transfer coefficient for convective mechanism. The

coolant surfaces which are in contact with the water

jacket walls shows higher temperature ranging from 190 OC to 290

OC. This is pretty severe condition though

engine cylinder head coolant outlet temperature is within

the safe range of operation (Figure 5). As the fluid passes

through the cooling jacket it gains heat and rises the

temperature on various irregular geometric positions.

Figure 2 also shows that the temperature of the coolant

varies rapidly from the hot wall side to the other side of

the channels. It is to be mentioned that after the high

temperature fluid layer near the hot walls, the

temperature of the coolant decreases within its cross

section of the flow stream and that is completely in the

safe zone.

Therefore, it is essential to manage a fluid flow through

the cooling jacket even after the engine is shut down to

avoid the further temperature rise and incipience of

severe boiling in full channel. External flow energy

should be obtained to manage this issue of fluid flow

after the shutdown of engine.

4.2 Velocity distribution

The velocity distribution of the coolant in the channel is

presented in the Figure 3. The simulated result

demonstrates that the flow field is distributed in a gradual

increase in velocity but in the lower mass flow rate.

Because of low mass flow around the end part of the

cylinder block it can’t take away the entire thermal load

imposed on it. The velocity increment or the mass flow

increment also increases the pressure losses in the

obstacles and flow uniformity is disturbed.

5. THEORETICAL ANALYSIS OF THE HEAT

TRANSFER IN THE COOLANT CHANNEL

Here the combustion wall temperature is considered as

mentioned by Stone(1992). And the coolant mass flow

rate is calculated as per the general energy equation,

. Where is the coolant mass flow rate

(kg/s), is the specific heat capacity of coolant (3.7

kj/kg.K), is the temperature difference between

engine coolant inlet and outlet, Qis the heat to be carried

away by the coolant. The total amount of heat to be

carried away for the conceived engine is obtained from

authors’ published article Hazrat et al.(2012).

Now, as per the average heat transfer coefficient found in

the Figure 4:

HTC for cylinder head jacket, hch= 3397 W/m2K and for

cylinder block side jacket, hcb= 3192.56 W/m2K

For both the cylinder block and head, the wall thickness

(Vs/As) is considered as characteristic length, lc = 6e-3m.

Adopting the material properties for cylinder head and

block, the following equation can be used to obtain

theoretical value of wall temperature inside the cooling

jacket hot side.

( ( ) )

( ) (

) , (8)

Where is the wall temperature at gas side, Tc is the

coolant inlet temperature, t is the reference time and in

this case it is t=1

Therefore, from equation (8),

For block, Tw,Fe= 355+(600-355)*exp{-

(3192.56)/(7870x448x6e-3}=565.68 K

And, for cylinder head, Tw,Al = 355+(600-355)*exp{-

(3397)/(2702x903x6e-3}=549.26 K

Figure 4 Heat transfer coefficient resulting from the

water cooling of the engine.

Figure 5 Coolant inlet and outlet temperature

distribution.

The conduction heat transfer equation from lump

capacitance also supports the higher temperature

distributions in the coolant side wall. So the conceived

CFD model can be considered as acceptable in some

extent though Stone(1992) mentioned that the inner wall

temperature should be 400K if the gas side wall

temperature is 600 in the spark ignition engines. But the

author did not mention the standard coolant flow rate to

be maintained in case of predefined heat removal

conditions.

6. CONCLUSION

The steady state heat transfer analysis of a commercial

passenger vehicle SI engine has been obtained through

out a complete high performance computing facility and

standard computational code to run the segregated

approach solvers to resolve the energy equations. The

result shows that though engine coolant outlet

temperature is within the safe region of the operation

principle, there is still a requirement of coolant flow

management inside the coolant channels more efficiently

so that the coolant can consume more heat and the

velocity pressure of the coolant should be managed

through improved design of the complex cooling jackets.

It has been shown that the solid wall thickness between

the combustion chamber wall and the cooling jacket

channel is also a factor for conduction heat transfer and

temperature distribution. In standard cases Stone (1992),

the wall thickness is considered as 10mm but here in the

conceived model it was 6mm only and therefore, the

coolant side wall temperature is also found as more

higher than as mentioned in the existing documents. But

a proper flow management of coolant through the

cooling jacket can reduce the severity due to temperature

increment in the coolant side. It may require dynamic

analysis and the authors are recently trying to establish a

full scale transient simulation for further analysis with a

sufficient computational facility.

ACKNOWLEDGEMENT

The authors would like to acknowledge the Techno fund

(TF001-2010) and Centre for Energy Sciences in

University of Malaya for providing complete facility to

conduct this research work.

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